“An equilateral triangle ABC has side length 2. A square,PQRS, is such that P lies on AB, Q lies on BC, and R and S lie on AC as shown. The points P, Q, R, and S move so that P, Q and R always remain on the sides of the triangle and S moves […]
Month: March 2023
Notice that given a right triangle, the side length of the inscribed square as shown above can be expressed using two side lengths of the right triangle. Look at the following diagram. It’s easy to see $ML:EF=CL:CF$, then $w:EF=(CF-w):CF$. Therefore we have $w=\frac{EF*CF}{EF+CF}$. This result is general. So, similarly, we can have the following equation […]
The CEMC gave 4 solutions. Here I want to discuss a more general method using analytic geometry and trignometry. Let’s place the diagram on a coordinate plane as shown below. Let $k$ be the slope of the line DP. The problem is actually asking for the maximum possible value of $k$ such that the conditions […]
I used to find the newest information about Real Madrid by Googling because Google provides a well-built widget. Recently I found a Restful API for football data, https://www.api-football.com/, which provides a free plan with 100 requests per day. With the server side running scheduled PHP scripts, I successfully implemented my own web page which automatically […]
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